Stress concentrations in fractured compact bone simulated with a special class of anisotropic gradient elasticity

Inna M. Gitman*, Harm Askes, Ellen Kuhl, Elias C. Aifantis

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

86 Citations (Scopus)

Abstract

A new format of anisotropic gradient elasticity is formulated and implemented to simulate stress concentrations in cortical bone. The higher-order effect of the underlying microstructure in cortical bone is accounted for through the introduction of two length scale parameters and associated strain gradient terms which modify the response of the standard elastic macroscopic continuum: one internal length related to the longitudinal fibres and the other related to the transversal Haversian systems. Thus, anisotropic material behaviour is not only included in the anisotropy of the elastic effective stiffness properties, but also in the anisotropic sources of heterogeneity. The model is validated numerically in tests with bone fractures in the longitudinal and the transversal directions. It was found that the dominant length scale effects are those that coincide with the direction of fracture, as defined by the orientation of a pre-existing crack.

Original languageEnglish
Pages (from-to)1099-1107
Number of pages9
JournalInternational journal of solids and structures
Volume47
Issue number9
DOIs
Publication statusPublished - 1 May 2010
Externally publishedYes

Keywords

  • Anisotropic gradient elasticity
  • Bone fracture
  • Bone stress concentrations
  • n/a OA procedure

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